The Goodison Park chief, who has now secured three European qualifications in four seasons, said: "We deserved it. We have been in the top five since new year, and our form has been coming back in recent games."
But Moyes accepts his side were sweating at one stage in the second half when they knew Aston Villa were winning at West Ham.
Moyes said: "We finished on a good note, with a good performance. All we lacked in the first half was the finish to underline our superiority at that stage.
"But I don't feel that we showed any nerves. We passed the ball well, and produced a really, really good performance. There was character and confidence.
"I wanted to win, I wanted 65 points. In many other seasons, that would have got us into the Champions League. When we did achieve that a couple of years ago, we did it with 61 points.
"This is one of my most pleasing seasons at the club, but I always prefer to think that the most pleasing season is still to come."